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Our numerical experiments show that the hierarchical matrix (H-matrix) solver is more efficient than the butterfly solver for electrically small problems, although the converse is true for sufficiently large problems. In this communication, we propose a hybrid matrix decomposition algorithm (HMDA) that combines the H-matrix and butterfly algorithms. In the HMDA, the H-matrix algorithm is employed to compress the lower–upper decomposition matrix in the lower levels, whereas the butterfly algorithm is adopted at the higher levels. Numerical examples demonstrate that the performance of the HMDA is similar to that of the H-matrix for electrically small problems and higher than the butterfly algorithm for electrically large problems.

In this communication, we present flexible and efficient solutions of large-scale electromagnetic scattering problems using the parallel discontinuous Galerkin (DG) surface integral equation (SIE) method. A simplified formulation of the conventional DG is used by removing the interior penalty term, thereby avoiding computational burden of the contour integral in the conventional DG. It is demonstrated numerically that the simplification causes convergence deficiency and changes the accuracy convergence rate of the solution for objects with sharp corners. The former is overcome by constructing preconditioners using the near-field matrix of the whole region, and the latter is proved to have a neglectable influence on the accuracy of the final solutions as long as normal mesh density requirement is satisfied. The wellscaling ternary parallelization approach of the multilevel fast multipole algorithm (MLFMA) is incorporated into the DG domain decomposition framework to reduce the complexity of the solution and strength its capability for large-scale problems, with the distribution of the nearfield-related calculation adjusted to adapt the nonuniform meshes for a better workload balance. Numerical results are included to validate the accuracy and demonstrate the scalability and versatility of the proposed method. In addition, we demonstrated the effectiveness of our algorithm by solving a high-definition complicated aircraft model with inlets and exhausts involving over one billion unknowns.

In this paper, a massively parallel approach of the multilevel fast multipole algorithm (PMLFMA) on graphics processing unit (GPU) heterogeneous platform, noted as GPU-PMLFMA, is presented for solving extremely large electromagnetic scattering problems involving tens of billions of unknowns, In this approach, the flexible and efficient ternary partitioning scheme is employed at first to partition the MLFMA octree among message passing interface (MPI) processes. Then the computationally intensive parts of the PMLFMA on each MPI process, matrix filling, aggregation and disaggregation, etc., are accelerated by using the GPU. Different parallelization strategies in coincidence with the ternary parallel MLFMA approach are designed for GPU to ensures a high computational throughput. Special memory usage strategy is designed to improve the computational efficiency and benefit data re-using. The CPU/GPU asynchronous computing pattern is designed with the OpenMP and CUDA respectively for accelerating the CPU and GPU execution parts and computation time overlapped. GPU architecture-based optimization strategies are implemented to further improve the computational efficiency. Numerical results demonstrate that the proposed GPU-PMLFMA can achieve over 3 times speed-up, compared with the 8-threaded conventional PMLFMA. Solutions of scattering by electrically large and complicated objects with about 24000 wavelengths and over 41.8 billion unknowns, are presented.

This article presents a new self-dual integral equation (SDIE) for electromagnetic scattering from arbitrarily impedance boundary condition (IBC) objects including partly coated objects. The proposed SDIE is constructed by using the combined field integral equation (CFIE) and IBC, shorted as C-SDIE. To overcome the difficulty of discontinuous surface impedance from nonuniform IBC/partly coated objects, the discontinuous Galerkin (DG) method is applied to discretize the C-SDIE. Numerical experiments confirm that the DG-C-SDIE has promising numerical performance in terms of accuracy and efficiency. Furthermore, the domain decomposition preconditioning based on DG is employed to further enhance the proposed DG-C-SDIE for large-scale, multi-scale objects. The numerical results demonstrate the capability of the proposed DG-C-SDIE.

A flexible and efficient Hierarchical LU ( $\mathcal{H}$ -LU)-based preconditioner ( $\mathcal{H}$ -LU-P) is presented for the hybrid finite element-boundary integral (FE-BI) multilevel fast multipole algorithm for solving three-dimensional scattering by inhomogeneous objects. The formulation of FE-BI is first approximated by using locally approximated integral operators for the BI part to construct a finite element method-absorbing boundary condition (FEM-ABC) based preconditioning matrix. Then, the preconditioning matrix equation is solved by the nested dissection accelerated $\mathcal{H}$ -LU-based fast direct solver. A semi-geometric clustering strategy is proposed to simplify the cluster tree-building procedure in representing the preconditioning matrix in the $\mathcal{H}$ -matrix form. Numerical results demonstrate that the $\mathcal{H}$ -LU-P outperforms other alternative preconditioners, based on multifrontal approach. The scattering by a large and complex aircraft model with a radome on its nose section is calculated, showing the capability and efficiency of the preconditioner.

In this paper, we present a flexible and efficient ternary parallelization approach for the multilevel fast multipole algorithm (MLFMA) for the solution of extremely large 3-D scattering problems with over 10 billion unknowns. In the ternary parallelization approach, a binary clustering tree of all the message passing interface (MPI) processes is built first. Then, the MLFMA tree is categorized into plane wave partitioning, hierarchical-structure partitioning, and box partitioning (BP) levels via a top–down approach to match the process clustering tree. Compared with the bottom–up approach, interprocess communications in the far interaction are reduced. An inner-group transition level is designed for switching partitions on the intermediate level between the hierarchical-structure partitioning and BP levels. The ternary strategy can realize as high parallel efficiency as the hierarchical partitioning strategy while maintaining flexibility in selecting the total number of processes. An auxiliary-tree-based parallel mesh refinement technique and a hybrid octree storage strategy are designed to facilitate the realization of fast full-wave simulation on a scale of over 10 billion unknowns with the ternary MLFMA. The accuracy of the solutions is validated by comparing the radar cross sections (RCSs) of a sphere of diameter 3042 wavelengths with 10 773 415 728 unknowns via the MLFMA and the Mie series, which is the largest number of unknowns to be computed via full wave numerical methods to date. Furthermore, the solutions for complicated objects, namely a ship and an aircraft model, both of which have maximum lengths that exceed 10 000 wavelengths and over 10 billion unknowns, are presented.

The integral equation method is one of the most successful computational models for microwave devices or integrated circuits in planar layered media. However, the efficient and accurate evaluation of the associated Green’s function consisting of Sommerfeld integrals (SIs) is still a remaining challenge. To mitigate this difficulty, this work proposes a spatial domain rational function fitting technique (RFFT) for SIs so that the approximation accuracy is controllable. In conjunction with an adaptive sampling strategy, the proposed RFFT minimizes the orders of rational functions, and the resultant SI evaluation efficiency is optimized. In addition, we investigate the semi-analytical singularity treatment for the rational expression of SIs in method of moment (MoM) implementation. Extensive simulation of representative planar devices validates the correctness of the proposed method and demonstrates its superior performance over conventional SI approximation methods.

A massively parallel approach of the multilevel fast multipole algorithm (MLFMA) on Deep Computing Unit (DCU) clusters using the Heterogeneous Interface for Portability (HIP) programming model and the Message Passing Interface (MPI) is presented (DCU-MLFMA). The proposed MPI-based multi-DCU parallel implementation is capable of solving challenging problems involving billions of unknowns with a significant speedup, compared with the conventional CPU-based ternary parallelization approach of MLFMA (CPU-MLFMA). Numerical results, including a ship model with length about 6000 wavelengths modeled with 2.6 billion unknowns, are given to demonstrate the capability, as well as the efficiency of the presented method.

Partly and nonuniform coated objects are one type of important targets in electromagnetic (EM) engineering, and their EM scattering characteristics are an aspect of great concern. To efficiently formulate the EM scattering problem of objects with partial nonuniform coating, we propose a new self-dual integral equation (SDIE) by combining the impedance boundary condition (IBC) and the combined field integral equation (CFIE) in a special way. Besides, the discontinuous Galerkin (DG) method is employed to discretize the new SDIE, which can effectively and flexibly deal with the problem of discontinuous surface impedances from nonuniform cases. Numerical experiments have proved the proposed DG-C-SDIE has much more stable convergence than existing integral equation methods for partly IBC objects while ensures high accuracy. To apply DG-C-SDIE method to analyze electrically large coated objects, we hereby further introduce a high-efficiency parallel algorithm of multilevel fast multipole based on MPI and OpenMP schemes to fast solve the matrix equation. With the aid of advanced computers, the parallel DG-C-SDIE method has the ability of dealing with large-scale objects with hundreds of wavelengths.

This paper presents a CPU/GPU asynchronous computing pattern based improved parallel multilevel fast multipole algorithm (MLFMA) for 3D electromagnetic scattering problems on GPU Cluster. In the presented parallel implementation, the matrix assembly process of the MLFMA is decomposed into CPU execution and GPU execution two parts. The former is performed on CPU using OpenMP multi-threading programming model, while the latter is performed on GPU with CUDA programming model. The execution time between the two parts is overlapped by using the feature of asynchronous execution between CPU and GPU. The performance of the proposed parallel implementation is investigated in terms of accuracy and efficiency. Numerical results show that, with the proposed parallel approach, over 10% speed-up can be attained, compared with the original parallel implementation.

Recently, Toll-like receptors (TLRs), a family of pattern recognition receptors, are reported as potential modulators for neuropathic pain, however, the desired mechanism is still unexplained. Here, we operated on the sciatic nerve to establish a pre-clinical rodent model of chronic constriction injury (CCI) in Sprague-Dawley rats, which were assigned into CCI and Decompression groups randomly. In Decompression group, the rats were performed with nerve decompression at post-operative week 4. Mechanical hyperalgesia and mechanical allodynia were obviously attenuated after a month. Toll-like receptor 5 (TLR5)-immunoreactive (ir) expression increased in dorsal horn, particularly in the inner part of lamina II. Additionally, substance P (SP) and isolectin B4 (IB4)-ir expressions, rather than calcitonin-gene-related peptide (CGRP)-ir expression, increased in their distinct laminae. Double immunofluorescence proved that increased TLR5-ir expression was co-expressed mainly with IB4-ir expression. Through an intrathecal administration with FLA-ST Ultrapure (a TLR5 agonist, purified flagellin from Salmonella Typhimurium, only the CCI-induced mechanical hyperalgesia was attenuated dose-dependently. Moreover, we confirmed that mu-opioid receptor (MOR) and phospho-protein kinase Cα (pPKCα)-ir expressions but not phospho-protein kinase A RII (pPKA RII)-ir expression, increased in lamina II, where they mostly co-expressed with IB4-ir expression. Go 6976, a potent protein kinase C inhibitor, effectively reversed the FLA-ST Ultrapure- or DAMGO-mediated attenuated trend towards mechanical hyperalgesia by an intrathecal administration in CCI rats. In summary, our current findings suggest that nerve decompression improves CCI-induced mechanical hyperalgesia that might be through the cross-talk of TLR5 and MOR in a PKCα-dependent manner, which opens a novel opportunity for the development of analgesic therapeutics in neuropathic pain.

We present in this paper a well-scaling parallel approach of the finite element-domain decomposition method (FEM-DDM) for solving large scale 3D scattering problems on many-core SW26010 processors. In this parallel approach, the whole solution domain is first decomposed in a two-level hierarchical way to minimize the inter process communication. Then the FEM matrix of each unit-level subdomain to be solved in the iterative solution of the interface problem from FEM-DDM, is solved via another sparse approximate inverse (SPAI) preconditioner accelerated iterative solver. This inner–outer iteration scheme is further accelerated by exploring many-core parallelization, with specially designed sparse matrix vector multiplications to improve the data access efficiency. The performance achievements are investigated in terms of accuracy, speed up, and scalability.

A flexible and efficient $\mathcal{H}$-LU-based preconditioner ($\mathcal{H}$-LU-P) is presented for the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for solving 3D scattering by inhomogeneous objects in this paper. The formulation of FE-BI is firstly approximated by using locally approximated integral operators for the BI part to construct a FEM-ABC based precondition matrix. Then the precondition matrix equation is solved by the nested dissection (ND) accelerated $\mathcal{H}$-LU-based fast direct solver. Performance of the $\mathcal{H}$-LU-P is studied numerically for different problems, including the quasi-static problem, 2D extended and 3D extended electrodynamic problems, etc. Numerical experiments show the $\mathcal{H}$-LU-P has an O(NlogN) memory complexity and an O(Nlog2N) CPU time complexity for the quasi-static, the 2D extended lossless and the 3D extended lossy problems. For the 3D extended lossless problems, the complexity is larger due to the increasing rank of the $\mathcal{H}$-LU, but it still outperforms alternative direct solvers, such as the popular multifrontal-based solver MUMPS. Large realistic scattering problems with more than ten million unknowns are calculated, including a honeycomb structure with 8100 elements, showing the capability and efficiency of our proposed preconditioner.

An efficient many-core parallel implementation of the multilevel fast multipole algorithm (MLFMA) for 3D electromagnetic scattering problems on SW26010 processor using the Athread programming model is presented. The performance achievements are investigated in terms of accuracy, speed up, and scalability. Numerical results demonstrate that our MLFMA implementation on SW26010 is capable for solving real-life problems with over one million unknowns with a remarkable speed-up(up to 8x).

TianQin is a planned space-based gravitational wave (GW) observatory consisting of three earth orbiting satellites with an orbital radius of about $10^5~{\rm km}$. The satellites will form a equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4}~{\rm Hz}$ and $1~{\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe or exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new generation $17~{\rm cm}$ single-body hollow corner-cube retro-reflector which has been launched with the QueQiao satellite on 21 May 2018; a new laser ranging station equipped with a $1.2~{\rm m}$ telescope has been constructed and the station has successfully ranged to all the five retro-reflectors on the Moon; and the TianQin-1 experimental satellite has been launched on 20 December 2019 and the first round result shows that the satellite has exceeded all of its mission requirements., 16 pages, 1 figure, invited article to a special section in PTEP

The TianQin-1 satellite (TQ-1), which is the first technology demonstration satellite for the TianQin project, was launched on 20 December 2019. The first round of experiment had been carried out from 21 December 2019 until 1 April 2020. The residual acceleration of the satellite is found to be about $1\times10^{-10}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$ and about $5\times10^{-11}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.05~{\rm Hz}\,$, measured by an inertial sensor with a sensitivity of $5\times10^{-12}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The micro-Newton thrusters has demonstrated a thrust resolution of $0.1~\mu{\rm N}$ and a thrust noise of $0.3~\mu{\rm N}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}$. The residual noise of the satellite with drag-free control is $3\times10^{-9}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The noise level of the optical readout system is about $30~{\rm pm}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The temperature stability at temperature monitoring position is controlled to be about $\pm3~{\rm mK}$ per orbit, and the mismatch between the center-of-mass of the satellite and that of the test mass is measured with a precision of better than $0.1~{\rm mm}$., Comment: 17 pages, 11 figures

A complete domain decomposition method (CDDM) of hybrid finite element-boundary integral (FE-BI) has been proposed for accurately analyzing multiscale and heterogeneous electromagnetic problem recently. In this communication, a cost-effective additive Schwarz preconditioner is proposed to further improve the capability of the CDDM-FEBI for electrically large scattering and radiation problems. This preconditioner is obtained by rarefying the FE-BI submatrix based on the characteristics of boundary integral equation. Numerical experiments demonstrate that the consumption of CPU time and memory for constructing the proposed preconditioner is greatly reduced comparing with the previous one under the premise of ensuring fast convergence.

We present in this paper a flexible and efficient ternary parallelization approach for MLFMA for the solution of extremely large 3D scattering problems that are modelled with over 10 billion unknowns. In the ternary parallelization approach, the MLFMA tree is categorized into plane wave partitioning, hierarchical-structure partitioning and box partitioning levels via a top-down approach. An inner-group transition level is designed for switching partitions on the intermediate level between the hierarchical-structure partitioning and box partitioning levels. The ternary strategy can realize as high parallel efficiency as the hierarchical partitioning strategy while maintaining flexibility in selecting the total number of processes. A scalable and efficient auxiliary-tree-based parallel mesh refinement technique and a simple and effective hybrid octree storage strategy are designed to facilitate the realization of fast full-wave simulation on a scale of over 10 billion unknowns with the ternary MLFMA. The accuracy of the solutions is evaluated by comparing the radar cross-sections (RCSs) of a sphere of diameter 3,042 wavelengths with 10,773,415,728 unknowns that were calculated via MLFMA and the Mie series. It is the largest number of unknowns solved to date. Furthermore, the solutions for complicated ob jects, namely, a ship and an aircraft with the size larger than 10 thousand wavelengths and over 10 billion unknowns, are presented.

A many-core implementation of the multilevel fast multipole algorithm (MLFMA) based on the Athread parallel programming model for computing electromagnetic scattering by a 3-D object on the homegrown many-core SW26010 CPU of China is presented. In the proposed many-core implementation of MLFMA, the data access efficiency is improved by using data structures based on the Structure-of-Array (SoA). The adaptive workload distribution strategies are adopted on different MLFMA tree levels to ensure full utilization of computing capability and the scratchpad memory (SPM). A double-buffering scheme is specially designed to make communication overlapped computation. The resulting Athread-based many-core implementation of the MLFMA is capable for solving real-life problems with over four hundred thousand unknowns with a remarkable speed-up. Numerical results show that with the proposed parallel scheme, a total speed-up larger than 7 times can be achieved, compared with the CPU master-core.

The nested dissection (ND) $\mathcal {H}$ -LU-based fast finite element (FE) direct solver is studied for scattering by large 3-D inhomogeneous objects. The special characteristics of the admissibility condition in FE method (FEM) are demonstrated comparing with those in the moment method. A weaker admissibility condition in FEM is proposed for higher efficiency than the conventional one. A better reduction scheme is presented for electrodynamic scattering problem. Numerical experiments show that our developed ND $\mathcal {H}$ -LU-based FE direct solver has O(NlogN) memory complexity and O(Nlog2N) CPU time complexity for a quasi-static problem, but a larger and irregular complexity for an electrodynamic problem. It has been compared with other most advanced direct sparse solvers and proved to have a better performance. A large realistic scattering problem with more than 10 million unknowns is calculated, showing the capability of our proposed ND-based $\mathcal {H}$ -LU direct FEM solver.

A flexible ternary parallelization approach of the multilevel fast multipole algorithm (MLFMA) is presented for the efficient solution of extremely large 3D scattering problems. In the ternary parallelization approach, the MLFMA tree is categorized into plane-wave partitioning, hierarchical-structure partitioning and box partitioning levels. A grouped transition level is specially designed to switch partitions on the intermediate level between the hierarchical-structure partitioning and box partitioning levels. The ternary strategy can achieve as high parallel efficiency as the hierarchical partitioning strategy while maintaining flexibility in choosing the number of processes. The accuracy of the solutions is demonstrated by comparing radar cross section (RCS) of a sphere with 2400 wavelengths diameter and 4,231,421,328 unknowns calculated by MLFMA and mie series. Furthermore, the solution of complicated objects with length 6131 wavelengths and 4,739,139,936 unknowns is also presented, which is the largest problem solved by MLFMA to date.

We present in this paper a flexible and efficient block diagonal symmetric Gauss-Seidel (BD-SGS) preconditioner for the hierarchical parallel FEM-DDM. In the hierarchical domain decomposition scheme, the whole FEM solution domain is first decomposed into large size subdomains with a total number equals to MPI processes. Then, each large subdomain is distributed to a MPI process and further decomposed into smaller ones to achieve good computation efficiency. Our preconditioner is based on this hierarchical parallel structure. It is specially designed to accelerate the convergence of iterative solution and reduce both the time and memory consumption of the reduced interface problems from FEM-DDM by constructing symmetric Gauss-Seidel preconditioner (SGS) for each large subdomain. Numerical examples are presented to demonstrate the efficiency, scalability, and capability of this specially designed BD-SGS preconditioner.

We present in this paper an efficient parallelization approach of the finite element domain decomposition method (FEM-DDM) for large scale 3D scattering problems. In this parallel FEM-DDM, the domain decomposition is done in a hierarchical way to minimize the inter-processor communication. In the hierarchical domain decomposition scheme, the whole FEM solution domain is first decomposed into large size subdomains with a total number equals to MPI processes. Then, each large subdomain is distributed to a MPI process and further decomposed into smaller ones to achieve good computation efficiency. Numerical examples are presented to demonstrate the accuracy, scalability, and capability of the proposed parallel FEM-DDM algorithm.

The nonconformal domain decomposition methods (DDMs) of the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) are presented for computing large electromagnetic scattering/radiation problems. The numerical performance of different transmission conditions between finite element method (FEM) subdomains, and FEM and BI domains is studied in this paper. The Dirichlet transmission condition (DTC) employed at the interface between FEM and BI domains has faster convergence than the Robin-type transmission condition, and this finding is different from the conclusions for the FEM DDMs published in the literature. Furthermore, the cement-element (CE)-based dual-primal finite element tearing and interconnecting (FETI-DP) DDM has faster convergence than the Lagrange-multiplier-based FETI-DP method under the FE-BI system, and is also different from that under the system of the FEM with the absorbing boundary condition (FEM-ABC). It shows that the DDMs of FE-BI-MLFMA have some essential differences from those of FEM-ABC. The analysis of these numerical phenomena is presented in this paper. Further comparison between the DDMs of FE-BI-MLFMA and FEM-ABC demonstrates that the DDMs of FE-BI-MLMFA have essential advantages over those of FEM-ABC. Various numerical experiments confirm the accuracy, efficiency, and flexibility of the nonconformal DDM of FE-BI-MLFMA, which is the CE-based FETI-DP DDM with DTC connecting FEM and BI.

This paper incorporates the compensated Mitzner boundary conditions CMBC into the hybrid finite element- boundary integral-multilevel fast multipole algorithm FE-BI-MLFMA for fast and accurate computation of scattering by three-dimensional inhomogeneous objects with thin dielectric structures. In this CMBC-FE-BI-MLFMA, each thin dielectric layer is reduced to an interface with zero thickness; then CMBC is applied to establish the relation of electromagnetic fields across the interfaces. This approach can reduce the amount of computation and remain the advantages of versatility, accuracy, and efficiency of the conventional FE-BI-MLFMA algorithm. The formulation of this CMBC-FE-BI-MLFMA is presented in this paper. An efficient preconditioner based on the sparse approximate inverse is employed and further parallelized on memory-distributed platforms. Numerical results are presented to demonstrate the accuracy, efficiency, and capability of the parallel CMBC-FE-BI-MLFMA. Copyright © 2016 John Wiley & Sons, Ltd.

The nested dissection (ND) H-LU-based fast finite element (FE) direct solver is studied for scattering by large 3D inhomogeneous objects. The mechanism of this fast FE direct solver is elucidated in reducing computational complexity from practical engineering point of view. The special characteristics of the admissibility condition in FEM are demonstrated comparing with those in the moment method. A weaker admissibility condition in FEM is proposed for higher efficiency than the conventional admissibility condition. The difference of numerical performance of this fast FE direct solver is in detail presented in reducing computational complexity for electrodynamic and quasi-static problems. Numerical experiments show that the H-LU has O(NlogN) memory complexity and O(Nlog2N) CPU time complexity for a quasi-static problem, but has a larger and irregular complexity for an electrodynamic problem. A large realistic scattering problem is calculated, showing the capability of our proposed ND based H-LU direct FEM solver.

A non-conformal finite element tearing and interconnecting-like FETI-like domain decomposition approach DDA of the hybrid finite element-boundary integral-multilevel fast multipole algorithm FE-BI-MLFMA is presented by integrating a series efficient techniques for computing electromagnetic scattering/radiation problems. The Robin transmission condition is employed to cement the non-conformal meshes on the interconnected surfaces between the interior and exterior regions and between sub-domains in the interior region. The FETI-like technique is applied to reduce the FE-BI matrix equation. Furthermore, a preconditioner is constructed to accelerate the convergent speed of this non-conformal FETI-like DDA. The numerical performance of the presented non-conformal FETI-like DDA-FE-BI-MLFMA is studied for scattering/radiation problems. Copyright © 2015 John Wiley & Sons, Ltd.

An accurate and efficient computational approach is presented for analyzing radiation characteristics of large antenna arrays with radome. This approach is based on the hybrid finite element- boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA). Unlike the conventional single- domain FE-BI-MLFMA, the whole domain of the antenna array with radome is separated into many disconnected domains. A large free space area unavoidable in the single-domain FE-BI-MLFMA is eliminated in this multi-domain FE-BI-MLFMA formulation, thus the number of unknowns is greatly reduced in the presented multi-domain FE-BI-MLFMA approach. Different from the single-domain FE- BI-MLFMA, many integral equations are required in this multi-domain FE-BI-MLFMA. The numerical experiment shows that the presented multi-domain FE-BI-MLFMA is more efficient than the single- domain one while maintaining the same accuracy. A whole complicated system of a slotted-waveguide array with radome mounted on an aircraft is analyzed to further demonstrate the generality and capability of the presented multi-domain FE-BI-MLFMA.

A domain-decomposition-based preconditioner (DDP) is presented for the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA). The formulation of FE-BI is first approximated by the finite element method (FEM) with absorbing boundary condition (ABC). Then this approximate FEM-ABC formulation is solved by using the finite element tearing and interconnecting method (FETI). Finally, an inner-outer iterative algorithm with variable convergence threshold is designed for FE-BI-MLFMA. Because of good numerical scalability of FETI and good approximation of FEM-ABC, this DDP-FE-BI-MLFMA performs well even for large lossless objects.

The hybrid method of the finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) has been recognized as one of the most powerful numerical methods for analyzing large inhomogeneous radiation/scattering problems. A domain decomposition algorithm (DDA) of FE-BI-MLFMA is presented in this paper by using the finite element tearing and interconnecting method (FETI). The formulation of DDA-FE-BI-MLFMA is presented and analyzed in detail. The numerical performance of DDA-FE-BI-MLFMA is investigated by numerical experiments from many aspects. It includes the convergence speed versus types of domain decomposition, number of subdomains, types and inhomogeneity of dielectrics involving in solved problems, and the scalability of DDA-FE-BI-MLFMA. The comparison of DDA and previous algorithms of FE-BI-MLMFMA is also carried out. Finally, the capability of DDA-FE-BI-MLFMA is shown for large inhomogeneous problems.

The hybrid flnite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is a powerful method for calculating scattering by inhomogeneous objects. However, the conventional FE-BI-MLFMA often sufiers from iterative convergence problems. A non-overlapping domain decomposition method (DDM) is applied to FE-BI-MLFMA to speed up the iterative convergence. Furthermore, a preconditioner based on absorbing boundary condition and symmetric successive over relaxation (ABC-SSOR) is constructed to further accelerate convergence of the DDM-FE-BI-MLFMA. Numerical experiments demonstrate the e-ciency of the proposed preconditioned DDM-FE-BI-MLFMA.

The domain decomposition methods (DDMs) have been applied to the hybrid finite element - boundary integral - multilevel fast multipole algorithm (FE-BI-MLFMA) and significantly improve its efficiency in recent years. These fast DDMs can be roughly classified into two types: Schwarz DDM and dual-primal finite element tearing and interconnecting (FETI-DP) DDM. This paper will give overview of the DDMs development of FE-BI-MLFMA. Then a uniform, consistent, and efficient formulation is presented and discussed for these fast DDMs of FE-BI-MLFMA. Their computational complexities are analyzed and studied numerically.

Using OpenMP to further accelerate the pure MPI parallel MLFMA, an efficient and flexible parallel multilevel fast multipole algorithm (MPI-OpenMP-MLFMA) is proposed. Compared with previous MPI parallel schemes, the MPI-OpenMP-MLFMA improves the load-balance and scalability greatly. The computational capability of the proposed MPI-OpenMP-MLFMA is demonstrated by computing scattering from two extremely large targets: a sphere with a diameter of 1200 wavelengths, modeled by 1,063,706,700 unknowns, and an airplane model with the largest dimension of 1600 wavelengths, involving 288,151,344 unknowns.